Question

determine whether y varies directly with x. if so, find the constant of variation and write the equation.​

Answer 1

For this case we have that if and it varies directly with x, we can write the equation as:

`y = kx`

Where:

k: It is the constant of proportionality.

According to the table:

`-3 = k (1)`

Clearing k:

`k = -3`

Then,
`y = -3x`

Answer:

Option C

Answer 2

y varies directly with x

`k = -3`

The equation is:

`y = -3x`

Explanation:

We can say that and it varies directly with x if it is fulfilled that

`y = kx`

Where k is a constant known as the constant of variation.

So

`(y)/(x) = k`

This means that if y varies with x then the division of y between x should always be equal to a constant value k.

We must test this for the values shown in the table

`(-3)/(1) = -3`

`(-9)/(3) = -3`

`(-15)/(5) = -3`

The quotient of
`(y)/(x)` is always equal to
`-3`. Then
`k = -3` and the variation of y with x is direct

The equation is:

`y = -3x`